/**
 * What is the greatest product of four adjacent numbers in any direction
 * (up, down, left, right, or diagonally) in the 20x20 grid?
 */

#include <iostream>
#include <utility>
#include "euler.h"

BEGIN_PROBLEM(11, solve_problem_11)
	PROBLEM_TITLE("Find the greatest product of four adjacent numbers in a grid")
	PROBLEM_ANSWER("70600674")
	PROBLEM_DIFFICULTY(1)
	PROBLEM_FUN_LEVEL(1)
	PROBLEM_TIME_COMPLEXITY("M*N")
	PROBLEM_SPACE_COMPLEXITY("N")
END_PROBLEM()

static char input[20][20] = 
{
	{ 8,2,22,97,38,15,0,40,0,75,4,5,7,78,52,12,50,77,91,8, },
	{ 49,49,99,40,17,81,18,57,60,87,17,40,98,43,69,48,4,56,62,0, },
	{ 81,49,31,73,55,79,14,29,93,71,40,67,53,88,30,3,49,13,36,65, },
	{ 52,70,95,23,4,60,11,42,69,24,68,56,1,32,56,71,37,2,36,91, },
	{ 22,31,16,71,51,67,63,89,41,92,36,54,22,40,40,28,66,33,13,80, },
	{ 24,47,32,60,99,3,45,2,44,75,33,53,78,36,84,20,35,17,12,50, },
	{ 32,98,81,28,64,23,67,10,26,38,40,67,59,54,70,66,18,38,64,70, },
	{ 67,26,20,68,2,62,12,20,95,63,94,39,63,8,40,91,66,49,94,21, },
	{ 24,55,58,5,66,73,99,26,97,17,78,78,96,83,14,88,34,89,63,72, },
	{ 21,36,23,9,75,0,76,44,20,45,35,14,0,61,33,97,34,31,33,95, },
	{ 78,17,53,28,22,75,31,67,15,94,3,80,4,62,16,14,9,53,56,92, },
	{ 16,39,5,42,96,35,31,47,55,58,88,24,0,17,54,24,36,29,85,57, },
	{ 86,56,0,48,35,71,89,7,5,44,44,37,44,60,21,58,51,54,17,58, },
	{ 19,80,81,68,5,94,47,69,28,73,92,13,86,52,17,77,4,89,55,40, },
	{ 4,52,8,83,97,35,99,16,7,97,57,32,16,26,26,79,33,27,98,66, },
	{ 88,36,68,87,57,62,20,72,3,46,33,67,46,55,12,32,63,93,53,69, },
	{ 4,42,16,73,38,25,39,11,24,94,72,18,8,46,29,32,40,62,76,36, },
	{ 20,69,36,41,72,30,23,88,34,62,99,69,82,67,59,85,74,4,36,16, },
	{ 20,73,35,29,78,31,90,1,74,31,49,71,48,86,81,16,23,57,5,54, },
	{ 1,70,54,71,83,51,54,69,16,92,33,48,61,43,52,1,89,19,67,48, },
};

static int find_max_product(int di, int dj)
{
	int max_prod = 0;
	for (int i = std::max(0,-3*di); i < std::min(20,20-3*di); i++)
	{
		for (int j = std::max(0,-3*dj); j < std::min(20,20-3*dj); j++)
		{
			int prod = 1;
			for (int k = 0; k < 4; k++)
			{
				prod *= input[i+k*di][j+k*dj];
			}
			max_prod = std::max(max_prod, prod);
		}
	}
	return max_prod;
}

static void solve_problem_11()
{
	int m1 = find_max_product(1,0);
	int m2 = find_max_product(0,1);
	int m3 = find_max_product(1,1);
	int m4 = find_max_product(1,-1);
	int m = std::max(std::max(m1,m2), std::max(m3,m4));
	std::cout << m << std::endl;
};